In the field of radar imaging, such as the radar imaging of objects moving through outer space, certain assumptions are often made regarding the motion state of the object. Specifically, the motion of the entire object is often modeled after the straight-line translation of a single point (usually the tip) of the object. More generally, the motion is modeled after the rotation of the object at a constant rate about an axis containing the radar line-of-sight, and for a time that is very short compared to the rotational period. These assumptions are intended to simplify estimation of the motion state of the object in order to ease, or even make possible, the calculations required in subsequent radar data image processing.
For example, in conventional Inverse Synthetic Aperture Radar (“ISAR”) systems, pulsed, wideband radar bursts are directed at a moving object and reflected back by “scatterers,” which may be moving in various directions and speeds relative to the center of mass (“CM”) of the object. When using the traditional assumption that scatterers on the object move in linear trajectories and thus have a constant radar phase history, the reflected radar data can be simply modeled as a linear function of time and frequency. The object motion is therefore relatively primitive and only estimates the velocity vector of a single point on the object at a nearly instantaneous moment in time. This is usually referred to in the prior art as “3D snapshot” imaging.
Unfortunately, 3D snapshot imaging, and other known ISAR data processing systems and methods, result in less than optimal resolution images of the object of interest that may be too coarse for a given imaging application (e.g., approximately 15 cm resolution for a radar with 1 GHz of bandwidth). The radar imaging interval must be very short to avoid “smearing” of the image over time, which often results from these conventional motion assumptions. Moreover, known radar imaging methods do not provide users with sufficient information about the true object motion, and more specifically, the rotation, of the object, which may be especially desired in some cases.
For example, in certain circumstances, the precise, combined, orbital-translational motion state, rotational motion state, and image of a projectile or satellite in exoatmospheric trajectory may be desired. In this case, the projectile may be traveling in torque-free motion (i.e., without external forces other than gravity) in an elliptical orbit about the Earth. The precise geometrical motion state (e.g., the precession frequency, spin frequency, half-cone angle, and direction of angular momentum vector) of this trajectory may be valuable for the purposes of discriminating between various types of objects moving through space, such as between randomly-tumbling objects and spin-precessing vehicles.
The systems and methods of the present disclosure solve one or more of the problems set forth above.